The present invention relates to a roller bearing used in places where abrupt acceleration/deceleration or load fluctuations are repeated such as in mill speed reducer used for various types of iron making rolling mills or a roller bearing for use in apparatus causing large vibrations such as axles of railway vehicles or vibrating screens, that is, it relates to a roller bearing for use in places where change of rotational speed of rollers occurs repeatedly or bearing radial vibrations are exerted repeatedly and, more in particular, it relates to a cage assembled in such a roller bearing.
Roller bearings have been used generally for supporting rotational shafts, for example, in various industrial machines such as iron making rolling mills or vehicles. A roller bearing comprises, for example, as shown in FIG. 1, an outer ring 1 having an outer ring raceway 1a at the inner circumferential surface, an inner ring 2 having an inner ring raceway 2a at the outer circumferential surface, a plurality of rollers 3 assembled such that they can roll between the outer ring raceway 1a and the inner ring raceway 2a, and a cage 4 interposed rotatably between the outer ring raceway 1a and the inner ring raceway 2a in a state of holding the plurality of the rollers 3.
The cage 4 comprises, as shown in FIG. 1 and FIG. 2, bar portions 7 each disposed between each of adjacent pockets 8 and opposed to the rolling surface of the roller, and a pair of circular portions 5, 6 connecting both axial sides of the bar portions 7 and axially opposed to the end surface of the roller.
A space surrounded with the pair of the circular portions 5, 6 and the bar portions 7, 7 is referred to as a pocket 8 for accommodating the roller 3, and the roller 3 is held rotatably in the cage 4 by providing a predetermined gap between the cage 4 and the roller 3.
In the subsequent description, for a cage in which the diameter is different between the pair of the circular portions 5, 6 as in a tapered roller bearing or a self aligning roller bearing, the circular portion of the cage having a larger diameter (larger diameter side) is referred to as a circular portion 5, while the circular portion thereof having a smaller diameter (smaller diameter side) is referred to as a second circular portion 6. Further, when the diameter is equal or nearly equal between the pair of the circular portions 5 and 6 as in a cylindrical roller bearing, the circular portion 5 and the second circular portion 6 are optionally specified.
Further, as shown in FIG. 14, roller bearings for use in various types of industrial machines described above include those having a plurality of rollers 3 arranged in two rows between the outer ring raceway 1a and the inner ring raceway 2a and having two cages 4 individually holding rollers 3 in each of the rows and disposed rotatably between the outer ring raceway 1a and the inner ring raceway 2a. 
The cage 4 is a comb-shaped cage, as shown in FIG. 14 and FIG. 15, respectively, comprising a circular portion 5 axially opposed to the end surface of the roller, and a plurality of bar portions 7 protruding from one axial side of the circular portion 5 and arranged circumferentially being opposed to the rolling surface of the roller. Also in this cage, a space surrounded by the circular portion 5 and the bar portions 7, 7 is referred to as a pocket 8 for accommodating the roller 3, and the roller 3 is held rotatably in the cage 4 by providing a predetermined gap between the cage 4 and the roller 3.
In the roller bearing having the two rows of rollers 3 as described above, when individual cage 4 is assembled on every row for each of the rollers 3 as shown in FIG. 14, a comb-shaped cage, a configuration thereof in which the bar portions 7 protrude only from one axial side of the circular portion 5 as shown in FIG. 15 is used. On the other hand, in a case where the rollers 3 in two rows are held by one cage, a comb-shaped cage, a configuration thereof in which bar portions 7 protrude respectively from both axial sides of the circular portion 5 as shown in FIG. 16 is used.
In the subsequent description, a comb-shaped cage of a configuration in which bar portions 7 protrude from one axial side of the circular portion 5 as shown in FIG. 15 is sometimes also referred to as a two component type cage, whereas a comb-shaped cage of a configuration in which bar portions 7 protrude from both axial sides of the circular portion 5 as shown in FIG. 16 is sometimes also referred to as a one component type cage.
By the way, when the roller bearing having each of the cages 4 as described above is used in places where abrupt acceleration/deceleration or load fluctuations are repeated such as in mill speed reducer used for various types of iron making rolling mills, since rotational speed of the rollers 3 changes abruptly, the roller 3 collides against the bar portion 7 of the cage 4 again and again. A load W in the circumferential direction by the collision is applied from the roller 3 to the bar portion 7 of the cage 4 as shown in FIG. 3 and FIG. 17 to deform the cage 4.
As a result, since the bending stress is loaded on the circular portions 5, 6 and the bar portion 7 repeatedly, cracks occur in the circular portions 5, 6 or the bar portions 7 which not only fractures the cage 4 but also sometimes makes the rotation of the bearing impossible during long time use.
Since the cracks occur at a connection section between the circular portions 5, 6 and the bar portions 7, it is necessary for preventing fracture of the cage 4 thereby preventing deterioration for the bearing life, to moderate the bending stress caused to the connection section by the load W in the circumferential direction.
Now, in a cage of a type having a pair of circular portions 5, 6 as shown in FIG. 1 and FIG. 2, the load W from the roller 3 exerts moment M1, M2 to each connection section between the circular portion 5 and the second circular portion 6, and the bar portions 7 respectively. Let the bending stress caused to an area A of the circular portion 5 in the connection section between the circular portion 5 and the bar portion 7 be denoted by "sgr"1, the bending stress caused to an area B of the second circular portion 6 in the connection section between the second circular portion 6 and the bar portion 7 be denoted by ("sgr"2, a bending stress caused to an area c of the bar portion 7 at the connection section between the circular portion 5 and the bar portion 7 be denoted by "sgr"3 and the bending stress caused to an area D of the bar portion 7 at the connection section between the second circular portion 6 and the bar portion 7 be denoted by "sgr"4, bending stresses "sgr"1 to a "sgr"4 are expressed by the following equations based on the conditions for the balance of forces in view of the strength of materials:
"sgr"1=M1e1/(2I1)xe2x80x83xe2x80x83(1)
"sgr"2=M2e2/(2I2)xe2x80x83xe2x80x83(2)
"sgr"3=M1e3/I3xe2x80x83xe2x80x83(3)
"sgr"4=M2e3/I3xe2x80x83xe2x80x83(4)
I1, I2 and I3 denote, respectively, moment of inertia of area for the circular portion 5, the second circular portion 6 and the bar portions 7, and moment of inertia of area I1, I2 and I3 are defined by the following equations:
I1=∫A1z12dA1xe2x80x83xe2x80x83(5)
I2=∫A2z22dA2xe2x80x83xe2x80x83(6)
I3=∫A3z32dA3xe2x80x83xe2x80x83(7)
A1, A2 and A3 in the equations (5) to (7) described above denote, respectively, the cross sectional areas for the circular portion 5, the second circular portion 6 and the bar portion 7.
Further, e1 to e3 in the equations (1) to (3) described above denote the maximum distances from the center of the graph to the cross sectional circumferential edge in each of the coordinate systems to be described later.
Further, the coordinate system for each of the moment of inertia of area I1, I2 and I3 is defined as follows. That is, as shown in FIG. 1, the moment of inertia of area I1 is in accordance with a y1-z1 orthogonal coordinate system, on the cross section of the circular portion 5, taking an axis y1 in the direction of a normal line for the conical surface or cylindrical surface that defines the outer diametrical surface of the cage and taking an axis z1 axially and in the direction of a tangential line for the conical surface or cylindrical surface, with respect to the center of the graph for the cross section as an origin, and this is a moment of inertia of area relative to a neutral axis vertical to the longitudinal direction of the bar portion 7. Further, the moment of inertia of area I2 is in accordance with a y2-z2 orthogonal coordinate system, on the cross section of the second circular portion 6, taking an axis y2 in the direction of a normal line for the conical surface or cylindrical surface and taking an axis z2 axially and in the direction of a tangential line for the conical surface or cylindrical surface, with respect to the center of the graph for the cross section as an origin, and this is a moment of inertia of area relative to a neutral axis vertical to the longitudinal direction of the bar portion 7. Further, the moment of inertia of area I3 is in accordance with a y3-z3 orthogonal coordinate system, on the cross section of the bar portion 7, taking an axis y3 in the direction of a normal line for the conical surface or cylindrical surface and taking an axis z3 circumferentially and in the direction of a tangential line for the conical surface or cylindrical surface, with respect to the center of the graph for the cross section as an origin, and this is a moment of inertia of area relative to a neutral axis vertical to the circumferential direction of the cage 4.
The longitudinal direction of the bar portion 7 means herein substantially the axial direction of the bearing.
Then, e1 in the equation (1) above represents the maximum value in the z1 coordinate at the cross sectional circumferential edge of the circular portion 5 on the side of the bar portion. Further, e2 in the equation (2) above represents the maximum value of the absolute value in the z2 coordinate at the cross sectional circumferential edge of the second circular portion 6 on the side of the bar portion. Further, e3 in the equation (3) above represents the maximum value of the absolute value in the z3 coordinate at the cross sectional circumferential edge of the bar portion 7.
Further, in the case of the cage as shown in FIG. 1 and FIG. 2 above, where the cross sectional shape of the bar portion 7 does not change in the axial direction, since the moment of inertia of area for the bar portion 7 does not also change in the axial direction, I3 is defined as the value of the moment of inertia of area. However, in a case where the cross sectional shape of the bar portion 7 changes in the axial direction, the moment of inertia of area of the bar portion 7 also changes in the axial direction. In this case, I3 in the tapered roller bearing is defined as an average value for the moment of inertia of area at one end of the bar portion 7 and the moment of inertia of area at the other end of the bar portion 7. Further, I3 in the cylindrical roller bearing and the self-aligning roller bearing is defined as an average value for the moment of inertia of area at one end of the bar portion 7, the moment of inertia of area at the other end of the bar portion 7 and the moment of inertia of area in the axial center of the bar portion 7.
Further, in the comb-shaped cage as shown in FIG. 14 and FIG. 15, moment M is exerted on a connection section between the circular portion 5 and bar portion 7 as shown in FIG. 17 by the load W in the circumferential direction caused by the collision of the roller 3. Let the bending stress caused to the area A of the circular portion 5 in the connection section between the circular portion 5 and the bar portion 7 be denoted by "sgr"1 and the bending stress caused to the area C of the bar portion 7 in the connection section between the circular portion 5 and the bar portion 7 be denoted by "sgr"3, each of the bending stresses "sgr"1 and "sgr"3 is represented by the following equation based on the conditions for the balance of forces in view of the strength of materials:
"sgr"1=Me1/(2I1)xe2x80x83xe2x80x83(8)
"sgr"3=Me3/I3xe2x80x83xe2x80x83(9)
I1 and I3 described above are, respectively, the moment of inertia of area for the circular portion 5 and the bar portion 7, and the moment of inertia of area I1 and I3 are defined by the following equations:
I1=∫A1z12dA1xe2x80x83xe2x80x83(10)
I3=∫A1z32dA3xe2x80x83xe2x80x83(11)
A1 and A3 in the equations (10) and (11) represent cross sectional areas for the circular portion 5 and the bar portion 7 respectively. Further, e1 and e3 in the equations (8), (9) above represent maximum distances from the center of the graph to the cross sectional circumferential edge in each of the coordinate systems to be described later.
Further, in the same manner as described above, coordinate system for each of the moment of inertia of area I1, I2 and I3 is defined as below. That is, as shown in FIG. 14, the moment of inertia of area I1 is in accordance with a y1-z1 orthogonal coordinate system, on the cross section of the circular portion 5, taking an axis y1 in the direction of a normal line for the cylindrical surface that defines the outer diametrical surface of the cage and taking an axis z1 axially and in the direction of a tangential line for the cylindrical surface, with respect to the center of the graph for the cross section as an origin, and this is a moment of inertia of area relative to a neutral axis vertical to the longitudinal direction of the bar portion 7. Further, as shown in FIG. 14, the moment of inertia of area I3 is in accordance with a y3-z3 orthogonal coordinate system, on the cross section of the bar portion 7, taking an axis y3 in the direction of a normal line for the cylindrical surface and taking an axis z3 circumferentially and in the direction of a tangential line for the cylindrical surface, with respect to the center of the graph for the cross section as an origin, and this is a moment of inertia of area relative to a neutral axis vertical to the circumferential direction of the cage.
Further, e1 in the equation (8) above represents the maximum value in the z1 coordinate in the cross sectional circumferential edge of the circular portion 5 on the side of the bar portion. Further, e3 in the equation (9) above represents the maximum value in the z3 coordinate in the cross sectional circumferential edge of the bar portion 7.
In the comb-shaped cage, the cross sectional shape of the bar portion 7 is generally unchanged in the axial direction but the cross sectional shape of the bar portion 7 may sometimes be changed in the axial direction such as, for example, in a cage for use in a self-aligning roller bearing. In such a case, I3 is defined as a moment of inertia of area at a connection section of the bar portion 7 with the circular portion 5.
As can be seen from the equation (1) to equation (4) or equation (8) and equation (9) above, it can be seen that each of the stresses "sgr"1 to "sgr"4 can be decreased by enlarging all the moment of inertia of area I1, I2 and I3.
On the other hand, in a case where the roller bearing having a cage 4 as shown in FIG. 27 is used in such places as undergoing large vibrations such as axles or driving devices of vehicles, iron making rolling mills or vibrating screens, the cage 4 vibrates repeatedly in the radial direction of the bearing and the bar portion 7 of the cage 4 collides with the roller 3 again and again. The collision exerts a radial load Wxe2x80x2 (radial direction) from the roller 3 to the bar portion 7 of the cage 4, and the cage 4 deforms as shown in FIG. 26. In this way, when the bending stress is loaded repeatedly to the pair of circular portions 5 and 6 and the bar portions 7, cracks occur in the circular portion 5 and 6 or the bar portions 7 during long time use, which not only fractures the cage 4 but also makes sometimes the bearing impossible to rotate.
Since the cracks occur in the connection section between the circular portions 5 and 6 and the bar portions 7, it is necessary for preventing the fracture of the cage 4 thereby preventing shortening of the bearing life, to moderate the bending stress caused to the connection section by the load Wxe2x80x2.
The cage 4 deforms as shown in FIG. 26 by the load Wxe2x80x2 from the roller 3. That is, the load Wxe2x80x2 is exerted on the axial center of bar portion 7, and moments M1xe2x80x2 and M2xe2x80x2 is exerted to each of the connection sections between the circular portion 5 and the second circular portion 6, and the bar portions 7 respectively and the bar portion 7 deforms by these loads and these moments as shown in FIG. 26. Further, loads xcexaWxe2x80x2 and (1xe2x88x92xcexa)Wxe2x80x2 is exerted to each of the connection sections between the circular portion 5 and the second circular portion 6, and the bar portions 7, and the circular portions 5 and 6 deform by these loads as shown in FIG. 26. In this case, xcexa is a constant of larger than 0 and smaller than 1, which can be determined by calculation in view of the strength of materials.
Let the bending stress caused to the area A of the circular portion 5 in the connection section between the circular portion 5 and the bar portion 7 be denoted by "sgr"1xe2x80x2, the bending stress caused to the area B of the second circular portion 6 in the connection section between the second circular portion 6 and the bar portion 7 be denoted by "sgr"2xe2x80x2, the bending stress caused to the area C of the bar portion 7 in the connection section between the circular portion 5 and the bar portion 7 be denoted by "sgr"3xe2x80x2, and the ending stress caused to the area D of the bar portion 7 in the connection section between the second circular portion 6 and the bar portion 7 be denoted by "sgr"4xe2x80x2, each of the bending stresses "sgr"1xe2x80x2 to "sgr"4xe2x80x2 can be represented by the following equations, for example, based on the conditions for the balance of forces in view of the strength of materials:
"sgr"1xe2x80x2=xcexaWxe2x80x2d1e1xe2x80x2/(4I1xe2x80x2)xe2x80x83xe2x80x83(12)
"sgr"2xe2x80x2=(1xe2x88x92xcexa)Wxe2x80x2d2e2xe2x80x2/(4I2xe2x80x2)xe2x80x83xe2x80x83(13)
"sgr"3xe2x80x2=M1xe2x80x2e3xe2x80x2/I3xe2x80x2xe2x80x83xe2x80x83(14)
"sgr"4xe2x80x2=M2xe2x80x2e3xe2x80x2/I3xe2x80x2xe2x80x83xe2x80x83(15)
The I1xe2x80x2, I2xe2x80x2 and I3xe2x80x2 represent, respectively, moment of inertia of area for the circular portion 5, the second circular portion 6 and the bar portion 7, and the moment of inertia of area I1xe2x80x2, I2xe2x80x2 and I3xe2x80x2 are defined by the following equations.
I1xe2x80x2=∫A1y12dA1xe2x80x83xe2x80x83(16)
I2xe2x80x2=∫A2y22dA2xe2x80x83xe2x80x83(17)
I3xe2x80x2=∫A3y32dA3xe2x80x83xe2x80x83(18)
A1, A2 and A3 in the equations (16) to (18) described above represent, respectively, the cross sectional areas for the circular portion 5, the second circular portion 6 and the bar portion 7. Further, e1xe2x80x2, e2xe2x80x2 and e3xe2x80x2 in the equations (12) to (15) described above represent the distances from the center of the graph to the cross sectional circumferential edge in each of the coordinate systems to be described later.
Further, the coordinate system for each of the moment of inertia of area I1xe2x80x2, I2xe2x80x2 and I3xe2x80x2 is defined as follows. That is, as shown in FIG. 27, the moment of inertia of area I1xe2x80x2 is in accordance with a y1-z1 orthogonal coordinate system, on the cross section of the circular portion 5, taking an axis Yi in the direction of a normal line for the conical surface or cylindrical surface that defines the outer diametrical surface of the cage and taking an axis z1 axially and in the direction of a tangential line for the conical surface or cylindrical surface, with respect to the center of the graph for the cross section as an origin, and this is a moment of inertia of area relative to a neutral axis parallel with the longitudinal direction of the bar portion 7. Further, the moment of inertia of area I2xe2x80x2 is in accordance with a y2-z2 orthogonal coordinate system, on the cross section of the second circular portion 6, taking an axis y2 in the direction of a normal line for the conical surface or cylindrical surface and taking an axis z2 axially and in the direction of a tangential line for the conical surface or cylindrical surface, with respect to the center of the graph for the cross section as an origin, and this is a moment of inertia of area relative to a neutral axis parallel with the longitudinal direction of the bar portion 7. Further, the moment of inertia of area I3xe2x80x2 is in accordance with a y3-z3 orthogonal coordinate system, on the cross section of the bar portion 7, taking an axis y3 in the direction of a normal line for the conical surface or cylindrical surface and taking an axis z3 circumferentially and in the direction of a tangential line for the conical surface or cylindrical surface, with respect to the center of the graph for the cross section as an origin, and this is a moment of inertia of area relative to a neutral axis parallel with the circumferential direction of the cage.
Then, e1xe2x80x2 in the equation (12) above represents the absolute maximum value in the y1 coordinate at the cross sectional circumferential edge of the circular portion 5. Further, e2xe2x80x2 in the equation (13) above represents the absolute maximum value in the y2 coordinate at the cross sectional circumferential edge of the second circular portion 6. Further, e3xe2x80x2 in the equation (14) above represents the absolute maximum value in the y3 coordinate in the cross sectional circumferential edge of the bar portion 7.
Further, in a case where the cross sectional shape of the bar portion 7 does not change in the axial direction, since the moment of inertia of area for the bar portion 7 does not also change in the axial direction, I3xe2x80x2 is defined with the value for the moment of inertia of area. However, in a case where the cross sectional shape of the bar portion 7 changes in the axial direction, the moment of inertia of area of the bar portion 7 also changes in the axial direction. In this case, I3xe2x80x2 in the tapered roller bearing is defined as an average value for the moment of inertia of area at one end of the bar portion 7 and the moment of inertia of area at the other end of the bar portion 7. Further, I3xe2x80x2 in the cylindrical roller bearing and self-aligning roller bearing is defined as an average value for the moment of inertia of area at one end of the bar portion 7, the moment of inertia of area at the other end of the bar portion 7 and the moment of inertia of area at the axial center of the bar portion 7.
As can be seen from the equation (12) to the equation (15), each of the stresses "sgr"1xe2x80x2 to "sgr"4xe2x80x2 decreases as all of the moment of inertia of area I1xe2x80x2, I2xe2x80x2 and I3xe2x80x2 increase.
Then, in the prior art, the moment of inertia of area I1, I2 and I3 and I1xe2x80x2, I2xe2x80x2 and I3xe2x80x2 are increased respectively by increasing all of the cross sections for the circular portions 5 and 6 and the bar portions 7, to improve the strength of the cage 4 thereby preventing occurrence of fracture.
In this case, while it was experientially recognized that the cross sectional area may be increased to improve the strength when the strength of the cage is insufficient but it was not designed by considering each of the moment of inertia of area for the circular portions 5 and 6 and the bar portions 7 and optimally determining the strength thereof.
Accordingly, in any type of the cages, when it is designed such that all the moment of inertia of area I1, I2 and I3 or all the moment of inertia of area I1xe2x80x2, I2xe2x80x2 and I3xe2x80x2 for the circular portions 5 and 6 and the bar portions 7 are increased, since the space volume for holding the rollers 3 (size and number of pockets 8) is decreased, the number of the rollers 3 that can be assembled into the bearing is decreased or the size of the roller 3 has to be reduced as the strength of the cage 4 is improved to bring about problem that the load capacity of the bearing is lowered. Further, it results in unnecessary increase of the weight of the cage.
Particularly, when it is intended to increase the strength to the composite load formed by both of the loads, namely, circumferential load and the radial load, all the moment of inertia of area I1, I2 and I3 and the moment of inertia of area I1xe2x80x2, I2xe2x80x2 and I3xe2x80x2 are increased and, as a result, the problem described above becomes conspicuous.
The present invention has been achieved while taking notice of such a problem and it is a object thereof to provide a cage for use in a roller bearing capable of improving the strength of the cage without lowering the load capacity of the bearing to which the cage is assembled.
It has been noted in each of the present inventions that the strength of the cage can be improved without lowering the load capacity of the bearing and preventing increase in the weight of the cage, by optimizing the bending stress of the circular portion and the bending strength of the bar portion such that they are not different greatly from each other while considering the direction of load exerted from the roller.
That is, for solving the foregoing subject, the invention described in claim 1 provides a cage for use in a roller bearing having a plurality of bar portions arranged circumferentially being opposed to the rolling surface of each of rollers and a pair of circular portions axially opposed to the end surface of each of the rollers and connecting both axial ends of the bar portions arranged in the circumferential direction, respectively, which satisfies at least one of the conditional equations;
the conditional equation:
0.8xe2x89xa6(I1/I2)xe2x89xa61.4
and
0.1xe2x89xa6(I1/I3)xe2x89xa63.0
or the conditional equation:
0.5xe2x89xa6(I1xe2x80x2/I2xe2x80x2)xe2x89xa62.7
and
0.2xe2x89xa6(I1xe2x80x2/I3xe2x80x2)xe2x89xa66.0
where
a circular portion having a larger or identical diameter, in the pair of the circular portions, is referred to as a circular portion, a circular portion having a smaller or identical diameter is referred to as a second circular portion, and it is defined that the moment of inertia of area for the circular portion relative to a neutral axis vertical to the longitudinal direction of the bar portion is I1, the moment of inertia of area for the second circular portion relative to a neutral axis vertical to the longitudinal direction of the bar portion is I2, the moment of inertia of area for the bar portion relative to a neutral axis vertical to the circumferential direction of the cage is I3, the moment of inertia of area for the circular portion relative to a neutral axis parallel with the longitudinal direction of the bar portion is I1xe2x80x2, the moment of inertia of area for the second circular portion relative to a neutral axis parallel with the longitudinal direction of the bar portion is I2xe2x80x2, and the moment of inertia of area for the bar portion relative to a neutral axis parallel with the circumferential direction of the cage is I3xe2x80x2.
As in a case of a cylindrical roller bearing, when the diameter is equal or nearly equal between the pair of the circular portions, a circular portion on optional side may be referred to as the circular portion and the other of them may be referred to as the second circular portion.
As in a cage for use in a roller bearing assembled in a tapered roller bearing, it is preferred as in the invention described in claim 2 to satisfy the conditions:
xe2x80x831.0xe2x89xa6(I1/I2)xe2x89xa61.4
and
0.1xe2x89xa6(I1/I3)xe2x89xa63.0.
Further, in a cage for use in a roller bearing assembled in a self-aligning roller bearing, it is preferred as in the invention described in claim 3 to satisfy the conditions:
0.8xe2x89xa6(I1/I2)xe2x89xa61.2
and
0.3xe2x89xa6(I1/I3)xe2x89xa63.0.
Further, in a case of a cage for use in a roller bearing assembled into a cylindrical roller bearing in which the diameter is equal or nearly equal between the pair of the circular portions, it is preferred as in the invention described in claim 4 to satisfy the condition:
0.1xe2x89xa6(I1/I3)xe2x89xa60.4.
Further, in a cage for use in a roller bearing assembled in a tapered roller bearing, it is preferred as in the invention described in claim 5 to satisfy the conditions:
1.0xe2x89xa6(I1xe2x80x2/I2xe2x80x2)xe2x89xa62.7
and
0.2xe2x89xa6(I1xe2x80x2/I3xe2x80x2)xe2x89xa66.0.
Further, in a cage for use in a roller bearing assembled in a self-aligning roller bearing, it is preferred as in the invention described in claim 6 to satisfy the conditions:
0.5xe2x89xa6(I1xe2x80x2/I2xe2x80x2)xe2x89xa61.7
and
0.2xe2x89xa6(I1xe2x80x2/I3xe2x80x2)xe2x89xa64.0.
Further, in a cage for use in a roller bearing assembled in a cylindrical roller bearing, it is preferred as in the invention described in claim 7 to satisfy the condition:
0.2xe2x89xa6(I1xe2x80x2/I3xe2x80x2)xe2x89xa60.8.
Further, in a cage for use in a roller bearing assembled in a tapered roller bearing, it is preferred as in the invention described in claim 8 to satisfy all of the conditions:
1.0xe2x89xa6(I1/I2)xe2x89xa61.4
and
0.1xe2x89xa6(I1/I3)xe2x89xa63.0,
1.0xe2x89xa6(I1xe2x80x2/I2xe2x80x2)xe2x89xa62.7
and
0.2xe2x89xa6(I1xe2x80x2/I3xe2x80x2)xe2x89xa66.0.
Further, in a cage for use in a roller bearing assembled in a self-aligning roller bearing, it is preferred as in the invention described in claim 9 to satisfy all of the conditions:
0.8xe2x89xa6(I1/I2)xe2x89xa61.2
and
0.3xe2x89xa6(I1/I3)xe2x89xa63.0
0.5xe2x89xa6(I1xe2x80x2/I2xe2x80x2)xe2x89xa61.7
and
0.2xe2x89xa6(I1xe2x80x2/I3xe2x80x2)xe2x89xa64.0.
Further, in a cage for use in a roller bearing assembled in a cylindrical roller bearing, it is preferred as in the invention described in claim 10 to satisfy both of the conditions:
xe2x80x830.1xe2x89xa6(I1/I3xe2x80x2)xe2x89xa60.4
and
0.2xe2x89xa6(I1xe2x80x2/I3xe2x80x2)xe2x89xa60.8.
In a case where the roller bearing as an object is a cylindrical roller bearing, it is usually: (I1/I2)≈1 but it is not always necessary to design the value as 1.
Then, the invention described in claim 11 provides a comb-shaped cage for use in a roller bearing having one circular portion axially opposed to the end surface of each of rollers and a plurality of bar portions protruding from one or both axial sides of the circular portion and arranged circumferentially while opposed to the rolling surface for each of the rollers, which satisfies the condition: 0.3xe2x89xa6(I1/I3)xe2x89xa61.6, where the moment of inertia of area for the circular portion relative to a neutral axis vertical to the longitudinal direction of the bar portion is I1 and the moment of inertia of area for the bar portion relative to a neutral axis vertical to the circumferential direction of the cage is I3.
In this case, in a cage in which bar portions protrude from only one axial side of the circular portion and which is assembled into a double row cylindrical roller bearing, it is preferred as in the invention described in claim 12 to satisfy the condition: 0.3xe2x89xa6(I1/I3)xe2x89xa60.9.
Further, in a cage in which the bar portions protrude from both axial sides of the circular portion and which is assembled into a double row cylindrical roller bearing, it is preferred as in the invention described in claim 13 to satisfy the condition: 0.7xe2x89xa6(I1/I3)xe2x89xa61.6.
Further, in a cage in which the bar portions protrude from only one axial side of the circular portion and which is assembled into a self-aligning roller bearing, it is preferred as in the invention described in claim 14 to satisfy the condition: 0.5xe2x89xa6(I1/I3)xe2x89xa61.5.
Further, in a cage in which the bar portions protrude from both axial sides of the circular portion and which is assembled into a self-aligning roller bearing, it is preferred as in the invention described in claim 15 to satisfy the condition: 0.3xe2x89xa6(I1/I3)xe2x89xa61.0.
The range (0.3 to 1.6) adopted for (I1/I3) in the invention described in claim 11 is included entirely in the range (0.1 to 3.0) adopted for (I1/I3) as in the invention described in Claim 1 and is specified with a narrower range.
In any of the present inventions described above, the strength of the cage is improved without lowering the load capacity of the bearing since the bending stress for each of the circular portions and the bending stress for the bar portion are designed such that they are not greatly different from each other in accordance with the type of the cage while considering the direction of load exerted from the roller.
Then, the ground is to be described.
At first, the ground for each of the inventions described in claims 1 to 10 is to be described with reference to FIG. 1 to FIG. 3.
Each of the loads in the circumferential direction and the radial direction of the bearing (radial direction) is exerted as an individual load or a composite load depending on the portion where the bearing is used and description of the grounds is to be made divisionally according to the direction of loads.
At first, description is to be made to a case where the load from the roller is applied in the circumferential direction.
For example, in a case where the bending stress "sgr"1 for the circular portion 5 is extremely larger compared with the bending stress "sgr"3 for the bar portion 7, that is, "sgr"1 greater than  greater than "sgr"3, since fracture of the cage 4 occurs at the area A of the circular portion 5, the strength can be improved by increasing the moment of inertia of area I1 for the circular portion 5 and, at the same time, decreasing the moment of inertia of area I3 for the bar portion 7 such that the space volume for holding the roller 3 is not decreased.
The moment of inertia of area can be increased usually by increasing the cross sectional area, while the moment of inertia of area can be decreased usually by decreasing the cross sectional area thereof. It is of course possible to change the moment of inertia of area by modifying the cross sectional shape.
On the contrary, in a case where the bending stress "sgr"3 for the bar portion 7 is extremely larger compared with the bending stress "sgr"1 for the circular portion 5, that is, "sgr"3 greater than  greater than "sgr"1, since fracture of the cage 4 occurs at the area C of the bar portion 7, the strength can be improved by increasing the moment of inertia of area I3 for the bar portion 7 and, at the same time, decreasing the moment of inertia of area I1 for the circular portion 5 such that the space volume for holding the roller 3 is not decreased.
That is, in a case where there is a significant difference between the bending stress "sgr"1 for the circular portion 5 and the bending stress "sgr"3 for the bar portion 7, fracture of the cage 4 can be prevented by decreasing this difference of the stresses without decreasing the number of rollers or the size of the rollers, namely, without lowering the load capacity of the bearing.
In the same manner, also in a case where there is a large difference between the bending stress "sgr"2 for the circular portion 6 and the bending stress "sgr"4 for the bar portion 7, fracture of the cage 4 can be prevented by decreasing the difference of the stresses without decreasing the number of rollers or the size of the rollers.
That is, it is considered in the present invention to apply an optimal design of improving the load capacity for the entire cage by increasing the moment of inertia of area only for the portion where the bending stress increases, instead of improving the strength of the cage 4 by increasing all the moment of inertia of area for each portion of the cage 4 as in the prior art.
From the view point described above, according to the present invention, (I1/I2) and (I1/I3) for minimizing the maximum value of the bending stress are defined based on values for dimensional factors for each of the portions within the adoptable range in view of the design.
Further, the case where the load is applied from the radial direction of the bearing (radial direction) is also studied with by the same concept as that for the load from the circumferential direction.
That is, in a case where the bending stress "sgr"1xe2x80x2 for the circular portion 5 is extremely larger compared with the bending stress "sgr"3xe2x80x2 for the bar portion 7 for instance, that is, "sgr"1xe2x80x2 greater than "sgr"3xe2x80x2, since fracture of the cage 4 occurs at the area A of the circular portion 5 shown in FIG. 26, the strength can be improved by increasing the moment of inertia of area I1xe2x80x2 for the circular portion 5 and, at the same time, by decreasing the moment of inertia of area I3xe2x80x2 for the bar portion 7 so as not to decrease the space volume for holding the roller 3.
The moment of inertia of area can be increased usually by increasing the cross sectional area, while the moment of inertia of area can be decreased usually by decreasing the cross sectional area thereof. It is of course possible to change the moment of inertia of area by modifying the cross sectional shape.
On the contrary, in a case where the bending stress "sgr"3xe2x80x2 for the bar portion 7 is extremely larger compared with the bending stress "sgr"1xe2x80x2 for the circular portion 5, that is, "sgr"3xe2x80x2 greater than  greater than "sgr"1xe2x80x2, since fracture of the cage 4 occurs at the area C for the bar portion 7 shown in FIG. 26, the strength can be improved by increasing the moment of inertia of area I3xe2x80x2 for the bar portion 7 and, at the same time, decreasing the moment of inertia of area I1xe2x80x2 for the circular portion 5 so as not to decrease the space volume for holding the roller 3.
That is, also in a case where there is a large difference between the bending stress aid for the circular portion 5 and the bending stress "sgr"3xe2x80x2 for the bar portion 7, the fracture of the cage 4 can be prevented by decreasing the difference of the stresses without decreasing the number of rollers or the size of the rollers, namely, without lowering the load capacity of the bearing.
In the same manner, also in a case where there is a large difference between the bending stress "sgr"2xe2x80x2 for the circular portion 6 and the bending stress "sgr"4xe2x80x2 for the bar portion 7, the fracture of the cage 4 can be prevented by decreasing the difference of the stresses without decreasing the number of rollers or the size of the rollers.
That is, it is considered in the present invention to apply optimal design of improving the load capacity for the entire cage by increasing the moment of inertia of area only for the portion in which the bending stress increases, instead of improving the strength of the cage 4 by increasing all the moment of inertia of area for each portions of the cage 4 as in the prior art.
Then, from the view point described above, (I1xe2x80x2/I2xe2x80x2) and (I1xe2x80x2/I3xe2x80x2) for minimizing the maximum value of the bending stress are defined in the present invention based on the values for dimensional factors for each of the portions within the adoptable range in view of the design.
The description has been made to a case where the circumferential load W and the radial load Wxe2x80x2 exert individually, but each of the concepts described above can be applied individually also to a cage to which loads from both of the directions are exerted, that is, a composite load comprising both of the loads are exerted repeatedly by decomposing the composite load into the circumferential component and the radial component.
Then, each of the critical meanings for the invention defined in claim 1 to claim 10 is to be described.
At first, the critical meaning relative to the circumferential load W is to be described.
When the relation between the non-dimensional maximum bending stress ("sgr"/"sgr"0), and (I1/I2), (I1/I3) is calculated on the basis of the model for the strength of materials, the result as shown in FIG. 4 was obtained.
The non-dimensional maximum bending stress ("sgr"/"sgr"0) is considered here because a non-dimensional concept can be applied to any magnitude of load, to improve the general utilizability.
Further, "sgr" described above is maximum among the bending stress "sgr"1 for the circular portion 5 in the connection section between the circular portion 5 and the bar portion 7, bending stress "sgr"2 for the second circular portion 6 in the connection section between the second circular portion 6 and the bar portion 7, and bending stress "sgr"3 for the bar portion 7 in the connection section between the circular portion 5 and the bar portion 7, bending stress "sgr"4 for the bar portion 7 in the connection section between the second circular portion 6 and the bar portion 7, based on the definition described above. Smaller a means less possibility of fracture of the cage 4 caused by collision between the roller 3 and the bar portion 7.
Further, "sgr"0 is the maximum bending stress caused to the bar portion 7 assuming a pair of the circular portions 5 and 6 as a rigid body.
The ("sgr"/"sgr"0) can be calculated if six parameters (I1/I2), (I1/I3), (e1/e2), (e1/e3), (d1/d2) and (d1/d3) are given.
In this case, d1 and d2 each represents the length of the circular portion 5 and the second circular portion 6, forming a roller containing pocket 8 and d3 is the length of the bar portion 7, as shown in FIG. 2.
Then, in most of cages for use in the roller bearing, since the dimensional specifications yield the following equations: (e1/e2)=0.2 to 1.8, (e1/e3)=0.2 to 1.2, (d1/d2)=0.8 to 1.4, (d1/d3)=0.5 to 3.0, each of the parameters: (e1/e2), (e1/e3), (d1/d2) and (d1/d3) is changed at random as shown in FIG. 4 within the ranges: (e1/e2)=0.2 to 1.8, (e1/e3)=0.2 to 1.2, (d1/d2)=0.8 to 1.4 and (d1/d3)=0.5 to 3.0 to determine the relation between (I1/I2) and (I1/I3) when ("sgr"/"sgr"0) takes the minimum value, and the minimum value ("sgr"/"sgr"0) as in FIG. 4.
In FIG. 4, the value ("sgr"/"sgr"0) is shown by a gray scale in which ("sgr"/"sgr"0) decreases as the color changes from white to black.
As can be seen from FIG. 4, if (I1/I2)=0.8 to 1.4 and (I1/I3)=0.1 to 3.0, they take optimal values among the possible ranges of design to minimize ("sgr"/"sgr"0) and it is possible to prevent the fracture of the cage for use in the roller bearing.
Based on this, it is defined in the present invention as: 0.8xe2x89xa6(I1/I2)xe2x89xa61.4 and 0.1xe2x89xa6(I1/I3)xe2x89xa63.0.
Then, symbol X in FIG. 4 is an example of determining (I1/I2) and (I1/I3) for minimizing ("sgr"/"sgr"0) in a case where (e1/e3) and (d1/d2) are not contained within the ranges: (e1/e3)=0.2 to 1.2, and (d1/d2)=0.8 to 1.4, respectively. (I1/I2) and (I1/I3) are not contained within the ranges: (I1/I2)=0.8 to 1.4 and (I1/I3)=0.1 to 3.0, and such cages are of an unpractical size with the value of (e1/e3) or (d1/d2) being not actually used.
Further, depending on the specifications of the roller bearing, the axial width of the circular portion 5 may be made relatively larger (to increase the cross section) than that of the second circular portion 6 as: (e1/e2)xe2x89xa71.
Then, a relation between (I1/I2) and (I1/I3) when ("sgr"/"sgr"0) takes a minimum value, and the minimum value ("sgr"/"sgr"0) was determined within the ranges: (e1/e2)=1 to 1.8, (e1/e3)=0.2 to 1.2, (d1/d2)=0.8 to 1.4 and (d1/d3)=0.5 to 3.0.
The result is shown in FIG. 5.
As can be seen from FIG. 5, if (I1/I2)=0.8 to 1.4 and (I1/I3)=0.1 to 0.6, ("sgr"/"sgr"0) is minimized and the value ("sgr"/"sgr"0) is smaller compared with the case of FIG. 4.
That is, in a case of specifying such that the width of the circular portion 5 is made larger than that of the second circular portion 6 without decreasing the size of the pocket 8, that is, (e1/e2)xe2x89xa71, it is particularly preferred to define as: (I1/I2)=0.8 to 1.4 and (I1/I3)=0.1 to 0.6 for preventing the fracture of the cage for use in the roller bearing and further optimization can be obtained.
Further, a tapered roller bearing is often used in such places where abrupt acceleration/deceleration or load fluctuations occur and the cage is liable to be fractured by collision between the roller 3 and the bar portion 7 as in mill speed reducer for various types of iron manufacturing rolling mills. Since most of tapered roller bearings are in the ranges: (e1/e2)=0.2 to 1.8, (e1/e3)=0.2 to 1.2, (d1/d2)=1.0 to 1.4 and (d1d3)=0.5 to 3.0, (e1/e2), (e1/e3), (d1/d2) and (d1/d3) are changed at random as parameters within these ranges and the relation between (I1/I2) and (I1/I3) when ("sgr"/"sgr"0) takes the minimum value, and the minimum value of ("sgr"/"sgr"0) was determined. The result is shown in FIG. 6.
As can be seen from FIG. 6, if (I1/I2)=1.0 to 1.4 and (I1/I3)=0.1 to 3.0, ("sgr"/"sgr"0) is minimized, and it is possible to prevent the fracture of the cage for use in the tapered roller bearing. That is, it can be seen that the cage for use in the tapered roller bearing is preferably designed optimally so as to provide: 1.0xe2x89xa6(I1/I2)xe2x89xa61.4 and 0.1xe2x89xa6(I1/I3)xe2x89xa63.0.
Further, among the tapered roller bearings, since those of particularly high frequency of use are in: (d1/d2)=1.0 to 1.2 and (d1/d3)=0.5 to 1.0, the relation between (I1/I2) and (I1/I3) when ("sgr"/"sgr"0) takes the minimum value, and the minimum value ("sgr"/"sgr"0) was determined within the ranges: (e1/e2)=0.2 to 1.8, (e1/e3)=0.2 to 1.2, (d1/d2)=1.0 to 1.2 and (d1/d3)=0.5 to 1.0, and the result shown in FIG. 7 was obtained.
As can be seen from FIG. 7, if (I1/I2)=1.0 to 1.2, and (I1/I3)=0.1 to 2.5, ("sgr"/"sgr"0) is minimized, which is preferred for preventing the fracture of the cage for use in the tapered roller bearing. That is, it can be seen that the cage for use in the tapered roller bearing is optimally designed preferably so as to provide: 1.0xe2x89xa6(I1/I2)xe2x89xa61.2 and 0.1xe2x89xa6(I1/I3)xe2x89xa62.5.
Further, depending on the specifications of the tapered roller bearing, the axial width of the circular portion 5 may be made larger than that of the second circular portion 6 as: (e1/e2)xe2x89xa71.0.
Then, the relation between (I1/I2) and (I1/I3) when ("sgr"/"sgr"0) takes a minimum value, and the minimum value ("sgr"/"sgr"0) was determined within the ranges: (e1/e2)=1.0 to 1.8, (e1/e3)=0.2 to 1.2, (d1/d2)=1.0 to 1.2, (d1/d3)=0.5 to 1.0, the result shown in FIG. 8 was obtained.
As can be seen from FIG. 8, if (I1/I2)=1.0 to 1.2 and (I1/I3)=0.1 to 0.6, ("sgr"/"sgr"0) is minimized and, since the value ("sgr"/"sgr"0) is smaller compared with that in FIG. 7, it can be seen that a further preferred optimal design can be obtained in view of prevention of the fracture of the cage for use in the tapered roller bearing, by setting as: (e1/e2)xe2x89xa71.0, that is, designing the axial width of the circular portion 5 larger than that of the second circular portion 6 and, at the same time, by setting as: 1.0xe2x89xa6(I1/I2)xe2x89xa61.2 and 0.1xe2x89xa6(I1/I3)xe2x89xa60.6.
Further, since most of cages for use in the self-aligning roller bearings are in the ranges: (e1/e2)=0.2 to 1.8, (e1/e3)=0.6 to 1.2, (d1/d2)=0.8 to 1.2, and (d1/d3)=0.5 to 3.0, (e1/e2), (e1/e3), (d1/d2) and (d1/d3) were changed at random as the parameters within these ranges and the relation between (I1/I2) and (I1/I3) when ("sgr"/"sgr"0) takes a minimum value, and the minimum value of ("sgr"/"sgr"0) was determined, the result shown in FIG. 9 was obtained.
As can be seen from FIG. 9, if (I1/I2)=0.8 to 1.2 and (I1/I3)=0.3 to 3.0, ("sgr"/"sgr"0) is minimized and it is possible to prevent the fracture of the cage for use in the self-aligning roller bearing. That is, it can be seen that 0.8xe2x89xa6(I1/I2)xe2x89xa61.2 and 0.3xe2x89xa6(I1/I3)xe2x89xa63.0 are desirable for the cage for use in the self-aligning roller bearing.
Further, among the self-aligning roller bearings, since those of particularly high frequency of use are in the ranges: (d1/d2)=0.9 to 1.1 and (d1/d3)=0.8 to 1.3, the relation between (I1/I2) and (I1/I3) when ("sgr"/"sgr"0) takes a minimum value, and the minimum value of ("sgr"/"sgr"0)was determined within the ranges: (e1/e2)=0.2 to 1.8, (e1/e3)=0.6 to 1.2, (d1/d2)=0.9 to 1.1 and (d1/d3)=0.8 to 1.3, the result as shown in FIG. 10 was obtained.
As can be seen from FIG. 10, if (I1/I2)=0.9 to 1.1 and (I1/I3)=0.3 to 2.5, ("sgr"/"sgr"0) is minimized, which is preferred in view of prevention of the fracture of the cage for use in the self-aligning roller bearing. That is, it can be seen that 0.9xe2x89xa6(I1/I2)xe2x89xa61.1 and 0.3xe2x89xa6(I1/I3)xe2x89xa62.5 is desirable in a case of the cage for use in the self-aligning roller bearing.
Further, depending on the specifications of the self-aligning roller bearing, the axial width of the circular portion 5 may be made larger than that of the second circular portion 6 to provide (e1/e2)xe2x89xa71.0.
Then, the relation between (I1/I2) and (I1/I3) when ("sgr"/"sgr"0) takes a minimum value, and the minimum value ("sgr"/"sgr"0) was determined within the ranges: (e1/e2)=1.0 to 1.8, (e1/e3)=0.6 to 1.2, (d1/d2)=0.9 to 1.1 and (d1/d3)=0.8 to 1.3, the result shown in FIG. 11 was obtained.
As can be seen from FIG. 11, if (I1/I2)=0.9 to 1.1 and (I1/I3)=0.3 to 0.6, since ("sgr"/"sgr"0) is minimized and the value ("sgr"/"sgr"0) is smaller compared with that in FIG. 10, it is preferred to specify as: (e1/e2)xe2x89xa71.0 and as: (I1/I2)=0.9 to 1.1 and (I1/I3)=0.3 to 0.6 for preventing the fracture of the cage for use in the self-aligning roller bearing. That is, by designing the axial width of the circular portion larger than that of the second circular portion, a further optimal design is possible as: 0.9xe2x89xa6(I1/I2)xe2x89xa61.1 and 0.3xe2x89xa6(I1/I3)xe2x89xa60.6.
Further, in the cage for use in the cylindrical roller bearing, since the cross sectional shape of the circular portion 5 is nearly equal the cross sectional shape of the circular portion 6, it can usually be regarded as: (e1/e2)=1.0 and (d1/d2)=1.0. Then, since most of the cages for use in the cylindrical roller bearing are within the ranges: (e1/e3)=0.2 to 0.8 and (d1/d3)=0.5 to 3.0, (e1/e3) and (d1/d3) were changed at random within the ranges, and the relation between (I1/I3) when ("sgr"/"sgr"0) takes a minimum value, and the minimum value of ("sgr"/"sgr"0) was determined, the result as shown in FIG. 12 was obtained. In most of the cages for use in the cylindrical roller bearings, since the cross sectional shape of the circular portion 5 and the cross section shape of the circular portion 6 is usually equal substantially, (I1I2) is about 1.0. Accordingly, it was defined as (I1/I2)=1.0.
As can be seen from FIG. 12, if (I1/I3)=0.1 to 0.4, ("sgr"/"sgr"0) is minimized, and it is possible to prevent the fracture of the cage for use in the cylindrical roller bearing. That is, it can be seen that the cage for use in the cylindrical roller bearing is optimally designed as: 0.1xe2x89xa6(I1/I3)xe2x89xa60.4.
Then, the critical meaning relative to the radial load of the bearing Wxe2x80x2 is to be described.
When the relation between the non-dimensional maximum bending stress ("sgr"xe2x80x2/"sgr"0xe2x80x2), and (I1xe2x80x2/I2xe2x80x2), (I1xe2x80x2/I3xe2x80x2) was calculated based on the model for the strength of materials, the result as shown in FIG. 28 was obtained.
The non-dimensional maximum bending stress ("sgr"xe2x80x2/"sgr"0xe2x80x2) is considered here because a non-dimensional concept can be applied to any magnitude of load, to improve the general utilizability.
Further, "sgr"xe2x80x2 described above is maximum among the bending stress "sgr"1xe2x80x2 for the circular portion 5 in the connection section between the circular portion 5 and the bar portion 7, bending stress "sgr"2xe2x80x2 for the second circular portion 6 in the connection section between the second circular portion 6 and the bar portion 7, bending stress "sgr"3 xe2x80x2 for the bar portion 7 in the connection section between the circular portion 5 and the bar portion 7, and bending stress "sgr"4xe2x80x2 for the bar portion 7 in the connection section between the second circular portion 6 and the bar portion 7, based on the definition described above. smaller "sgr" means less possibility of fracture of the cage 4 caused by collision between the roller 3 and the bar portion 7.
Further, "sgr"0xe2x80x2 is the maximum bending stress caused to the bar portion 7 regarding a pair of the circular portions 5 and 6 as a rigid body.
("sgr"xe2x80x2/"sgr"0xe2x80x2) can be calculated if six parameters (I1xe2x80x2/I2xe2x80x2), (I1xe2x80x2/I3xe2x80x2), (e1xe2x80x2/e2xe2x80x2), (e1xe2x80x2/e3xe2x80x2), (d1/d2) and (d1/d3) are given.
In this case, as shown in FIG. 26, d1 and d2 each represents the length of the circular portion 5 and the second circular portion 6, forming a roller holding pocket 8 respectively, and d3 is the length of the bar portion 7.
Then, in most of cages for use in the roller bearing, since possible ranges in view of the dimensional factors are, respectively, (e1xe2x80x2/e2xe2x80x2)=0.2 to 1.2, (e1xe2x80x2/e3xe2x80x2)=0.8 to 4.2, (d1/d2)=0.8 to 1.4 and (d1/d3)=0.5 to 3.0, each of the parameters: (e1xe2x80x2/e2xe2x80x2), (e1xe2x80x2/e3xe2x80x2), (d1/d2) and (d1/d3) was changed at random within the ranges: (e1xe2x80x2/e2xe2x80x2)=0.2 to 1.2, (e1xe2x80x2/e3xe2x80x2)=0.8 to 4.2, (d1/d2)=0.8 to 1.4 and (d1/d3)=0.5 to 3.0 in FIG. 28, and the relation between (I1xe2x80x2/I2xe2x80x2) and (I1xe2x80x2/I3xe2x80x2) when ("sgr"xe2x80x2/"sgr"0xe2x80x2) takes a minimum value, and the minimum value of ("sgr"xe2x80x2/"sgr"0xe2x80x2) was determined as in FIG. 28.
In FIG. 28, the value ("sgr"xe2x80x2/"sgr"0xe2x80x2) is shown by a gray scale in which ("sgr"xe2x80x2/"sgr"0xe2x80x2) decreases as the color changes from white to black.
As can be seen from FIG. 28, if (I1xe2x80x2/I2xe2x80x2)=0.5 to 2.7 and (I1xe2x80x2/I3xe2x80x2)=0.2 to 6.0, they take optimal values among the possible ranges of design to minimize ("sgr"xe2x80x2/"sgr"0xe2x80x2), and it is possible to prevent the fracture of the cage for use in the roller bearing.
Based on this, it is defined in the present invention as: 0.5xe2x89xa6(I1xe2x80x2/I2xe2x80x2)xe2x89xa62.7 and 0.2xe2x89xa6(I1xe2x80x2/I3xe2x80x2)xe2x89xa66.0.
Then, symbol X in FIG. 4 is an example of determining (I1xe2x80x2/I2xe2x80x2) and (I1xe2x80x2/I3xe2x80x2) for minimizing ("sgr"xe2x80x2/"sgr"0xe2x80x2) in a case where any of (e1xe2x80x2/e2xe2x80x2), (e1xe2x80x2/e3xe2x80x2), (d1/d2) and (d1/d3) is not contained in the ranges: (e1xe2x80x2/e2xe2x80x2)=0.2 to 1.2, (e1xe2x80x2/e3xe2x80x2)=0.8 to 4.2, (d1/d2)=0.8 to 1.4 and (d1/d3)=0.5 to 3.0. (I1xe2x80x2/I2xe2x80x2) and (I1xe2x80x2/I3xe2x80x2) are not contained in the range (I1xe2x80x2/I2xe2x80x2)=0.5 to 2.7 and (I1xe2x80x2/I3xe2x80x2)=0.2 to 6.0, and such cages are of a not-practical size, with the value for any of (e1xe2x80x2/e2xe2x80x2), (e1xe2x80x2/e3xe2x80x2), (d1/d2) or (d1/d3) being not actually used.
Further, among roller bearings, since those of particularly high frequency of use in apparatus causing large vibrations such as axles of railway vehicles and vibrating screens are within the ranges: (e1xe2x80x2/e2xe2x80x2)=0.2 to 1.2, (e1xe2x80x2/e3xe2x80x2)=0.8 to 3.0, (d1/d2)=0.9 to 1.3 and (d1/d3)=0.5 to 1.2, each of the parameters (e1xe2x80x2/e2xe2x80x2), (e1xe2x80x2/e3xe2x80x2), (d1/d2) and (d1/d3) was changed at random within this range and the relation between (I1xe2x80x2/I2xe2x80x2) and (I1xe2x80x2/I3xe2x80x2) when ("sgr"xe2x80x2/"sgr"0xe2x80x2) takes the minimum value, and the minimum value ("sgr"xe2x80x2/"sgr"0xe2x80x2) was determined. The result is shown in FIG. 29.
As can be seen from FIG. 29, if (I1xe2x80x2/I2xe2x80x2)=0.8 to 2.2 and (I1xe2x80x2/I3xe2x80x2)=0.2 to 4.0, ("sgr"xe2x80x2/"sgr"0xe2x80x2) is minimized and this is desirable for preventing the fracture of the cage for use in the roller bearing. That is, it can be seen that the cage for use in the roller bearing of particularly high frequency of use in apparatus causing large vibrations such as axles of railway vehicles and vibrating screens is preferably designed optimally so as to provide: 0.8xe2x89xa6(I1xe2x80x2/I2xe2x80x2)xe2x89xa62.2 and 0.2xe2x89xa6(I1xe2x80x2/I3xe2x80x2)xe2x89xa64.0.
Further, since most of cages for use in the tapered roller bearings are within the ranges: (e1xe2x80x2/e2xe2x80x2)=0.2 to 1.0, (e1xe2x80x2/e3e)=0.8 to 4.2, (d1/d2)=1.0 to 1.4, and (d1/d3)=0.5 to 3.0, (e1xe2x80x2/e2xe2x80x2), (e1xe2x80x2/e3xe2x80x2), (d1/d2) and (d1/d3) were changed at random as the parameters within these ranges and the relation between (I1xe2x80x2/I2xe2x80x2) and (I1xe2x80x2/I3xe2x80x2) when ("sgr"xe2x80x2/"sgr"0xe2x80x2) takes the minimum value, and the minimum value of ("sgr"xe2x80x2/"sgr"0xe2x80x2) was determined. The result is shown in FIG. 30.
As can be seen from FIG. 30, if (I1xe2x80x2/I2xe2x80x2)=1.0 to 2.7 and (I1xe2x80x2/I3xe2x80x2)=0.2 to 6.0, ("sgr"xe2x80x2/"sgr"0xe2x80x2) is minimized, and it is possible to prevent the fracture of the cage for use in the tapered roller bearing. That is, it can be seen that the cage for use in the tapered roller bearing is optimally designed preferably so as to provide: 1.0xe2x89xa6(I1xe2x80x2/I2xe2x80x2)xe2x89xa62.7 and 0.2xe2x89xa6(I1xe2x80x2/I3xe2x80x2)xe2x89xa66.0.
Further, among the tapered roller bearings, since those used in places of particularly high frequency of use in apparatus causing large vibrations such as axles of railway vehicles and vibrating screens are within the ranges: (e1xe2x80x2/e2xe2x80x2)=0.2 to 1.0, (e1xe2x80x2/e3xe2x80x2)=0.8 to 2.0, (d1/d2)=1.1 to 1.3 and (d1/d3)=0.5 to 1.0, (e1xe2x80x2/e2xe2x80x2), (e1xe2x80x2/e3xe2x80x2), (d1/d2) and (d1/d3) were changed at random wherein this range as the parameters and the relation between (I1xe2x80x2/I2xe2x80x2) and (I1xe2x80x2/I3xe2x80x2) when ("sgr"xe2x80x2/"sgr"0xe2x80x2) takes the minimum value, and the minimum value of ("sgr"xe2x80x2/"sgr"0xe2x80x2) was determined, the result as shown in FIG. 31 was obtained.
As can be seen from FIG. 31, if (I1xe2x80x2/I2xe2x80x2)=1.3 to 2.2 and (I1xe2x80x2/I3xe2x80x2)=0.8 to 4.0, ("sgr"xe2x80x2/"sgr"0xe2x80x2) is minimized, which is preferred in view of prevention of the fracture of the cage for use in the tapered roller bearing. That is, it can be seen that the cage for use in the tapered roller bearing of particularly high frequency of use in apparatus causing large vibrations such in axles of railway vehicles and vibrating screens is optimally designed further preferably so as to provide: 1.3xe2x89xa6(I1xe2x80x2/I2xe2x80x2)xe2x89xa62.2 and 0.8xe2x89xa6(I1xe2x80x2/I3xe2x80x2)xe2x89xa64.0.
Further, since most of cages for use in the self-aligning roller bearings are within the ranges: (e1xe2x80x2/e2xe2x80x2)=0.2 to 1.2, (e1xe2x80x2/e3xe2x80x2)=1.0 to 3.0, (d1/d2)=0.8 to 1.2, and (d1/d3)=0.5 to 3.0, when (e1xe2x80x2/e2xe2x80x2), (e1xe2x80x2/e3xe2x80x2), (d1/d2) and (d1/d3) were changed at random as the parameters within these ranges and the relation between (I1xe2x80x2/I2xe2x80x2) and (I1xe2x80x2/I3xe2x80x2) where ("sgr"xe2x80x2/"sgr"0xe2x80x2) takes the minimum value and the minimum value, ("sgr"xe2x80x2/"sgr"0xe2x80x2) was determined, the result shown in FIG. 32 was obtained.
As can be seen from FIG. 32, if (I1xe2x80x2/I2xe2x80x2)=0.5 to 1.7 and (I1xe2x80x2/I3xe2x80x2)=0.2 to 4.0, ("sgr"xe2x80x2/"sgr"0xe2x80x2) is minimized, and it is possible to prevent the fracture of the cage for use in the self-aligning roller bearing. That is, it can be seen that 0.5xe2x89xa6(I1xe2x80x2/I2xe2x80x2)xe2x89xa61.7 and 0.2xe2x89xa6(I1xe2x80x2/I3xe2x80x2)xe2x89xa64.0 are preferred in the cage for use in the self-aligning roller bearing.
Further, among the self-aligning roller bearings, since those used in places of particularly high frequency of use in apparatus causing large vibrations such as axles of railway vehicles and vibrating screens are within the ranges: (e1xe2x80x2/e2xe2x80x2)=0.8 to 1.2, (e1xe2x80x2/e3xe2x80x2)=1.0 to 3.0 (d1/d2)=0.9 to 1.1 and (d1/d3)=0.8 to 1.2, (e1xe2x80x2/e2xe2x80x2), (e1xe2x80x2/e2xe2x80x2), (d1/d2) and (d1/d3) were changed at random as the parameters within these ranges and the relation between (I1xe2x80x2/I2xe2x80x2) and (I1xe2x80x2/I3xe2x80x2) when ("sgr"xe2x80x2/"sgr"0xe2x80x2) takes the minimum value and the minimum value ("sgr"xe2x80x2/"sgr"0xe2x80x2) was determined. The result is shown in FIG. 33.
As can be seen from FIG. 33, if (I1xe2x80x2/I2xe2x80x2)=0.8 to 1.3 and (I1xe2x80x2/I3xe2x80x2)=0.5 to 4.0, ("sgr"xe2x80x2/"sgr"0xe2x80x2) is minimized, which is desirable for preventing the fracture of the cage for use in the self-aligning roller bearing. That is, it can be seen that 0.8xe2x89xa6(I1xe2x80x2/I2xe2x80x2)xe2x89xa61.3 and 0.5xe2x89xa6(I1xe2x80x2/I3xe2x80x2)xe2x89xa64.0 are further desirable for the cage used for the self-aligning roller bearing, particularly, for those used in places of high frequency of use in apparatus causing large vibrations such as axles of railway vehicles and vibrating screens.
Further, in the cage for use in the cylindrical roller bearings, since the cross sectional shape of the circular portion 5 and the cross sectional shape of the circular portion 6 are nearly equal, it can usually be considered as: (e1xe2x80x2/e2xe2x80x2)=1.0 and (d1/d2)=1.0. Then, since most of cages for use in the cylindrical roller bearings are within the ranges: (e1xe2x80x2/e3xe2x80x2)=0.8 to 3.4 and (d1/d3)=0.5 to 3.0, (e1xe2x80x2/e3xe2x80x2) and (d1/d3) were changed at random within these ranges and the relation between (I1xe2x80x2/I3xe2x80x2) when ("sgr"xe2x80x2/"sgr"0xe2x80x2) takes the minimum value, and the minimum value of ("sgr"xe2x80x2/"sgr"0xe2x80x2) was determined, the result shown in FIG. 34 was obtained. Further, in the cage for use in the cylindrical roller bearing, since the cross sectional shape of the circular portion 5 and the cross sectional shape of the circular portion 6 are usually identical substantially, (I1xe2x80x2/I2xe2x80x2) was about 1.0. Therefore, it was determined as (I1xe2x80x2/I2xe2x80x2)=1.0.
As can be seen from FIG. 34, if (I1xe2x80x2/I3xe2x80x2)=0.2 to 0.8, ("sgr"xe2x80x2/"sgr"0xe2x80x2) is minimized, and it is possible to prevent the fracture of the cage for use in the cylindrical roller bearing. That is, it can be seen that the cage for use in the cylindrical roller bearing is preferably designed optimally so as to provide: 0.2xe2x89xa6(I1xe2x80x2/I3xe2x80x2)xe2x89xa60.8.
Further, among the cylindrical roller bearings, since those used in places of particularly high frequency of use in apparatus causing large vibrations such as axles of railway vehicles and vibrating screens are within the ranges: (e1xe2x80x2/e3xe2x80x2)=0.8 to 1.6 and (d1/d3)=0.5 to 1.0, (e1xe2x80x2/e3xe2x80x2) and (d1/d3) were changed at random as the parameters within the ranges, and the relation between (I1xe2x80x2/I3xe2x80x2) when ("sgr"xe2x80x2/"sgr"0xe2x80x2) takes the minimum value and the minimum value ("sgr"xe2x80x2/"sgr"0xe2x80x2) was determined. The result is shown in FIG. 35. In the cage for use in the cylindrical roller bearing, since the cross sectional shape of the circular portion 5 and the cross sectional shape of the circular portion 6 are usually identical substantially, (I1xe2x80x2/I2xe2x80x2) is about 1.0. Therefore, it is defined as (I1xe2x80x2/I2xe2x80x2)=1.0.
As can be seen from FIG. 35, if (I1xe2x80x2/I3xe2x80x2)=0.2 to 0.4, ("sgr"xe2x80x2/"sgr"0xe2x80x2) is minimized, which is preferred for preventing the fracture of the cage for use in the cylindrical roller bearing. That is, it can be seen that 0.2xe2x89xa6(I1xe2x80x2/I3xe2x80x2)xe2x89xa60.4 is further desirable for the cage for use in the cylindrical roller bearing, particularly those used in places of high frequency in use in apparatus causing large vibrations such as axles of railway vehicles and vibrating screens.
It has been described to the case in which the load in the rotational direction (circumferential direction) of the roller and the load in the bearing radial direction of the cage are exerted individually in the foregoing description but, for improving the strength to the exertion of the load composed of both of the loads, (I1/I2), (I1/I3) and (I1xe2x80x2/I2xe2x80x2), (I1xe2x80x2/I3xe2x80x2) may be set so as to be within the ranges described above.
Then, description is to be made for the ground of the inventions in claims 11 to 15 with reference to FIGS. 14 to 17.
For example, in a case where the bending stress "sgr"1 for the circular portion 5 is extremely larger compared with the bending stress "sgr"3 for the bar portion 7, that is, "sgr"1 greater than  greater than "sgr"3, since fracture of the cage 4 occurs at the area A of the circular portion 5, the strength can be improved by increasing the moment of inertia of area I1 for the circular portion 5 and, at the same time, decreasing the moment of inertia of area I3 for the bar portion 7 such that the space volume for holding the roller is not decreased. The moment of inertia of area can be decreased usually by decreasing the cross sectional area thereof. It is of course possible to change the moment of inertia of area by modifying the cross sectional shape.
On the contrary, in a case where the bending stress "sgr"3 for the bar portion 7 is extremely larger compared with the bending stress "sgr"1 for the circular portion 5, that is, "sgr"3 greater than  greater than "sgr"1, since fracture of the cage 4 occurs at the area C of the bar portion 7, the strength can be improved by increasing the moment of inertia of area I3 for the bar portion 7 and, at the same time, decreasing the moment of inertia of area I1 of the circular portion 5 such that the space volume for holding the roller 3 is not decreased.
That is, in a case where there is a significant difference between the bending stress "sgr"1 for the circular portion 5 and the bending stress "sgr"3 for the bar portion 7, fracture of the cage 4 can be prevented by decreasing the difference of the bending stresses without decreasing the number of rollers or the size of the rollers. It is considered in present invention to apply an optimal design of improving the load capacity for the entire cage by increasing the moment of inertia of area only for the portion where the bending stress increases, instead of improving the strength of the cage 4 by increasing all the moment of inertia of area for each portion of the cage 4 as in the prior art.
From the view point described above, according to the present invention, (I1/I3) for minimizing the maximum value of the bending stress is defined based on the values for dimensional factors for each of the portions within the adoptable range in view of the design.
Then, the critical meanings for the inventions defined in claim 11 to claim 15 are to be described.
When the relation between the non-dimensional maximum bending stress ("sgr"/"sgr"0) and (I1/I3) is calculated on the basis of the model in view of the strength of materials, a result as shown in FIG. 18 was obtained. The non-dimensional maximum bending stress ("sgr"/"sgr"0) is considered here because a non-dimensional concept can be applied to any magnitude of load, to improve the general utilizability.
Further, "sgr" described above is maximum among the bending stress "sgr"1 for the circular portion 5 in the connection section between the circular portion 5 and the bar portion 7 and the bending stress "sgr"3 for the bar portion 7 in the connection section between the circular portion 5 and the bar portion 7, based on the definition described above. Smaller "sgr" means less fracture of the cage 4 caused by collision between the roller 3 and the bar portion 7. Further, "sgr"0 is the maximum bending stress caused to the bar portion 7 regarding a pair of circular portion 5 as a rigid body.
The ("sgr"/"sgr"0) can be calculated if three parameters (I1/I3), (e1/e3) and (d1/d3) are given.
Then, as shown in FIG. 15, d1 is a circumferential distance between two adjacent bar portions 7, 7 in the circumferential direction. The two bar portions 7, 7 adjacent in the circumferential direction protrude from the identical axial side of the cage relative to the circular portion 5 in a case where the cage is a two component type as shown in FIG. 15 but protrude from the axial sides of the cage opposite to each other relative to the circular portion 5 in a case where the cage is a one component type as shown in FIG. 16. Further, d3 is an axial distance from a position at which load W is exerted by collision with the roller 3 (position of arrow F in FIG. 15) on the lateral surface of the bar portion 7 opposing to the rolling surface of the roller 3 to the lateral side of the circular portion 5 opposing to the end surface of the roller 3.
Then, in most of cages for use in the roller bearing, since (e1/e3)=0.6 to 3.2 and (d1/d3)=0.2 to 3.0, each of the parameters: (e1/e3) and (d1/d3) is changed at random within the ranges: (e1/e3)=0.6 to 3.2 and (d1/d3)=0.2 to 3.0 to determine the relation between (I1/I3) when ("sgr"/"sgr"0) takes the minimum value, and the minimum value of ("sgr"/"sgr"0) as in FIG. 18.
As can be seen from FIG. 18, if (I1/I3)=0.3 to 1.6, it takes an optimal value among the possible range of design to minimize ("sgr"/"sgr"0), and it is possible to prevent the fracture of the cage for use in the roller bearing.
Based on this, it is defined in the present invention as: 0.3xe2x89xa6(I1/I3)xe2x89xa61.6.
Then, symbol X in FIG. 18 is an example of determining (I1/I3) for minimizing ("sgr"/"sgr"0) in a case where (e1/e3) is not contained within the ranges: (e1/e3)=0.6 to 3.2. In this case, (I1/I3) is not contained within the ranges: (I1/I3)=0.8 to 1.6 and such a cage is of an unpractical size with the value of (e1/e3) being not used actually.
Further, a double row cylindrical roller bearing or a self-aligning roller bearing is often used in such places where extremely large loads are applied on the bearing as in various kinds of iron making rolling mills. In most of double row cylindrical roller bearings,. since the ranges are: (e1/e3)=0.6 to 1.8, and (d1/d3)=0.6 to 2.2 in a case where the cage is a two component type, (e1/e3) and (d1/d3) are changed at random as parameters within the ranges described above and the relation between (I1/I3) when ("sgr"/"sgr"0) takes a minimum value, and the minimum value of ("sgr"/"sgr"0) was determined. The result is shown in FIG. 19.
As can be seen from FIG. 19, if (I1/I3)=0.3 to 0.9, ("sgr"/"sgr"0) is minimized, and it is possible to prevent the fracture of the cage for use in the double row cylindrical roller bearing. That is, it can be seen that the two component type cage for use in the double row cylindrical roller bearing is preferably designed optimally so as to provide: 0.3xe2x89xa6(I1/I3)xe2x89xa60.9.
Further, in most of double row cylindrical roller bearings, since the ranges are: (e1/e3)=1.4 to 3.2, and (d1/d3)=0.6 to 1.8 in a case where the cage is a one component type, (e1/e3) and (d1/d3) are changed at random as parameters within the ranges described above and the relation between (I1/I3) when ("sgr"/"sgr"0) takes a minimum value, and the minimum value of ("sgr"/"sgr"0) was determined. The result is shown in FIG. 20.
As can be seen from FIG. 20, if (I1/I3)=0.7 to 1.6, ("sgr"/"sgr"0) is minimized, and it is possible to prevent the fracture of the cage for use in the double row cylindrical roller bearing. That is, it can be seen that the one component type cage for use in the double row cylindrical roller bearing is preferably designed optimally so as to provide: 0.7xe2x89xa6(I1/I3)xe2x89xa61.6.
Further, in most of self-aligning roller bearings, since the ranges are: (e1/e3)=1.0 to 3.0, and (d1/d3)=0.6 to 3.0 in a case where the cage is a two component type, (e1/e3) and (d1/d3) are changed at random as parameters within the ranges described above and the relation between (I1/I3) when ("sgr"/"sgr"0)takes a minimum value, and the minimum value of ("sgr"/"sgr"0) was determined. The result is shown in FIG. 21.
As can be seen from FIG. 21, if (I1/I3)=0.5 to 1.5, ("sgr"/"sgr"0) is minimized, and it is possible to prevent the fracture of the cage for use in the self-aligning roller bearing. That is, it can be seen that the two component type cage for use in the self-aligning roller bearing is preferably designed optimally so as to provide: 0.5xe2x89xa6(I1/I3)xe2x89xa61.5.
Further, in most of self-aligning roller bearings, since the ranges are: (e1/e3)=0.6 to 2.0, and (d1/d3)=0.2 to 1.2 in a case where the cage is one component type, (e1/e3) and (d1/d3) are changed at random as parameters within the ranges described above and the relation between (I1/I3) when ("sgr"/"sgr"0) takes a minimum value, and the minimum value of ("sgr"/"sgr"0) was determined. The result is shown in FIG. 22.
As can be seen from FIG. 22, if (I1/I3)=0.3 to 1.0, ("sgr"/"sgr"0) is minimized, and it is possible to prevent the fracture of the cage for use in the self-aligning roller bearing. That is, it can be seen that the one component type cage for use in the self-aligning roller bearing is preferably designed optimally so as to provide: 0.3xe2x89xa6(I1/I3)xe2x89xa61.0.
As can be seen from FIG. 18 to FIG. 22, as the value (I1/I3) is larger, the value ("sgr"/"sgr"0) also increases to provide an apparent disadvantage and reduced the impact durability. Accordingly, it is desirable to keep the value (I1/I3) smaller depending on the conditions used.